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arXiv:1802.08673 · The European Physical Journal Special Topics

Generalized entropies in quantum and classical statistical theories

M. Portesi, Federico Holik, Pedro W. Lamberti, G. M. Bosyk, Guido Bellomo, Steeve Zozor

Published Sep 1, 2018• 8 citations
arXivHTMLPDF
DOI
10.1140/epjst/e2018-00108-1

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Entropy Beyond the Second Law presents a coherent formulation of all aspects of thermodynamics and statistical mechanics with entropy as the unifying theme. This includes formulating equilibrium theory and explaining the role of the Second Law in establishing the equilibrium state. It also establishes the foundations of non-equilibrium theory by generalizing the concept of entropy in an appropriate way. Finally, it addresses the relationship between classical and quantum statistical mechanics by invoking the collapse of the wave function into entropy states. A secondary purpose is to increase the understanding of entropy and the Second Law, and to correct misapprehensions and errors that have arisen over the years.
In these notes we will give an overview and road map for a definition and characterization of (relative) entropy for both classical and quantum systems. In other words, we will provide a consistent treatment of entropy which can be applied within the recently developed Orlicz space based approach to large systems. This means that the proposed approach successfully provides a refined framework for the treatment of entropy in each of classical statistical physics, Dirac's formalism of Quantum Mechanics, large systems of quantum statistical physics, and finally also for Quantum Field Theory.
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